Systems and methods for improved sustainment of a high performance FRC and high harmonic fast wave electron heating in a high performance FRC

ABSTRACT

Systems and methods that facilitate forming and maintaining FRCs with superior stability as well as particle, energy and flux confinement and, more particularly, systems and methods that facilitate forming and maintaining FRCs with elevated system energies and improved sustainment utilizing neutral beam injection and high harmonic fast wave electron heating.

CROSS-REFERENCE TO RELATED APPLICATIONS

The subject application is a continuation of PCT Patent Application No. PCT/US17/61860, filed Nov. 15, 2017, which claims priority to U.S. Provisional Patent Application No. 62/422,525, filed on Nov. 15, 2016, both of which are incorporated by reference herein in their entireties for all purposes.

FIELD

The embodiments described herein relates generally to magnetic plasma confinement systems having a field reversed configuration (FRC) and, more particularly, to systems and methods that facilitate forming and maintaining FRCs with superior stability as well as particle, energy and flux confinement and, more particularly, to systems and methods that facilitate high harmonic fast wave electron heating in FRCs.

BACKGROUND INFORMATION

The Field Reversed Configuration (FRC) belongs to a class of magnetic plasma confinement topologies known as compact toroids (CT). The FRC exhibits predominantly poloidal magnetic fields and possesses zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The attractions of such a configuration are its simple geometry for ease of construction and maintenance, a natural unrestricted divertor for facilitating energy extraction and ash removal, and very high β (β is the ratio of the average plasma pressure to the average magnetic field pressure inside the FRC), i.e., high power density. The high β nature is advantageous for economic operation and for the use of advanced, aneutronic fuels such as D-He³ and p-B¹¹.

The traditional method of forming an FRC uses the field-reversed θ-pinch technology, producing hot, high-density plasmas (see A. L. Hoffman and J. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is the translation-trapping method in which the plasma created in a theta-pinch “source” is more-or-less immediately ejected out one end into a confinement chamber. The translating plasmoid is then trapped between two strong mirrors at the ends of the chamber (see, for instance, H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current drive methods may be applied such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating, etc. This separation of source and confinement functions offers key engineering advantages for potential future fusion reactors. FRCs have proved to be extremely robust, resilient to dynamic formation, translation, and violent capture events. Moreover, they show a tendency to assume a preferred plasma state (see e.g. H. Y. Guo, A. L. Hoffman, K. E. Miller, and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significant progress has been made in the last decade developing other FRC formation methods: merging spheromaks with oppositely-directed helicities (see e.g. Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) and by driving current with rotating magnetic fields (RMF) (see e.g. I. R. Jones, Phys. Plasmas 6, 1950 (1999)) which also provides additional stability.

Recently, the collision-merging technique, proposed long ago (see e.g. D. R. Wells, Phys. Fluids 9, 1010 (1966)) has been significantly developed further: two separate theta-pinches at opposite ends of a confinement chamber simultaneously generate two plasmoids and accelerate the plasmoids toward each other at high speed; they then collide at the center of the confinement chamber and merge to form a compound FRC. In the construction and successful operation of one of the largest FRC experiments to date, the conventional collision-merging method was shown to produce stable, long-lived, high-flux, high temperature FRCs (see e.g. M. Binderbauer, H. Y. Guo, M. Tuszewski et al., Phys. Rev. Lett. 105, 045003 (2010)).

FRCs consist of a torus of closed field lines inside a separatrix, and of an annular edge layer on the open field lines just outside the separatrix. The edge layer coalesces into jets beyond the FRC length, providing a natural divertor. The FRC topology coincides with that of a Field-Reversed-Mirror plasma. However, a significant difference is that the FRC plasma has a β of about 10. The inherent low internal magnetic field provides for a certain indigenous kinetic particle population, i.e. particles with large larmor radii, comparable to the FRC minor radius. It is these strong kinetic effects that appear to at least partially contribute to the gross stability of past and present FRCs, such as those produced in the collision-merging experiment.

Past FRC experiments have tended to be dominated by convective losses with energy confinement largely determined by particle transport. Particles diffuse primarily radially out of the separatrix volume, and are then lost axially in the edge layer. Accordingly, FRC confinement depends on the properties of both closed and open field line regions. The particle diffusion time out of the separatrix scales as τ_(⊥)˜a²/D_(⊥) (a˜r_(s)/4, where r_(s) is the central separatrix radius), and D_(⊥) is a characteristic FRC diffusivity, such as D_(⊥)˜12.5 pie, with pie representing the ion gyroradius, evaluated at an externally applied magnetic field. The edge layer particle confinement time τ_(∥) is essentially an axial transit time in past FRC experiments. In steady-state, the balance between radial and axial particle losses yields a separatrix density gradient length δ˜(D_(⊥)τ_(∥))^(1/2). The FRC particle confinement time scales as (τ_(⊥)τ_(∥))^(1/2) for past FRCs that have substantial density at the separatrix (see e.g. M. Tuszewski, “Field Reversed Configurations,” Nucl. Fusion 28, 2033 (1988)).

Another drawback of prior FRC system designs is the lack of efficient electron heating regimes other than neutral beam injection, which tends to have poor electron heating efficiency due to the mechanism of power damping on electrons through ion-electron collision.

In light of the foregoing, it is, therefore, desirable to improve the sustainment of FRCs in order to use steady state FRCs with elevated energy systems as a pathway to a reactor core for fusion of light nuclei for the future generation of energy.

SUMMARY

The present embodiments provided herein are directed to systems and methods that facilitate forming and maintaining FRCs with superior stability as well as particle, energy and flux confinement and, more particularly, to systems and methods that facilitate forming and maintaining FRCs with elevated system energies and improved sustainment and, more particularly, to systems and methods that facilitate high harmonic fast wave electron heating in FRCs. According to an embodiment of the present disclosure, a method for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising forming an FRC about a plasma in a confinement chamber, injecting a plurality of neutral beams into the FRC plasma at an angle toward the mid-plane of the confinement chamber, and launching high harmonic fast waves in radio frequency ranges into the FRC plasma for electron heating in the core of the FRC plasma.

According to a further embodiment of the present disclosure, the method further includes maintaining the FRC at or about a constant value without decay and elevating the plasma electron temperature to above about 1.0 keV by launching high harmonic fast waves in radio frequency ranges into the FRC plasma at an angle from the mid through plane of the confinement chamber.

Heating of electrons via high harmonic fast waves in radio frequency ranges advantageously reduces fast ions charge-exchange loss and improves plasma confinement, as well as enhances plasma current drive efficiency, which goes up with electron temperature Te.

According to a further embodiment of the present disclosure, the method further comprising injecting compact toroid (CT) plasmas from first and second CT injectors into the FRC plasma at an angle towards the mid-plane of the confinement chamber, wherein the first and second CT injectors are diametrically opposed on opposing sides of the mid-plane of the confinement chamber.

According to an embodiment of the present disclosure, a system for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising a confinement chamber, first and second diametrically opposed FRC formation sections coupled to the confinement chamber first and second, first and second divertors coupled to the first and second formation sections, one or more of a plurality of plasma guns, one or more biasing electrodes and first and second mirror plugs, wherein the plurality of plasma guns includes first and second axial plasma guns operably coupled to the first and second divertors, the first and second formation sections and the confinement chamber, wherein the one or more biasing electrodes being positioned within one or more of the confinement chamber, the first and second formation sections, and the first and second divertors, and wherein the first and second mirror plugs being positioned between the first and second formation sections and the first and second divertors, a gettering system coupled to the confinement chamber and the first and second divertors, a plurality of neutral atom beam injectors coupled to the confinement chamber and angled toward a mid-plane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc coils positioned around the confinement chamber, the first and second formation sections, and the first and second divertors, and first and second set of quasi-dc mirror coils positioned between the first and second formation sections and the first and second divertors, and one or more antennas coupled to the confinement chamber to launch high harmonic fast waves in radio frequency ranges for electron heating in the core of the FRC plasma within the confinement chamber.

According to a further embodiment of the present disclosure, the system further comprising first and second compact toroid (CT) injectors coupled to the confinement chamber at an angle towards the mid-plane of the confinement chamber, wherein the first and second CT injectors are diametrically opposed on opposing sides of the mid-plane of the confinement chamber.

The systems, methods, features and advantages of the example embodiments will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional methods, features and advantages be included within this description, and be protected by the accompanying claims. It is also intended that the claims are not limited to require the details of the example embodiments.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings, which are included as part of the present specification, illustrate the presently example embodiments and, together with the general description given above and the detailed description of the example embodiments given below, serve to explain and teach the principles of the present embodiments.

FIG. 1 illustrates particle confinement in the present FRC system under a high performance FRC regime (HPF) versus under a conventional FRC regime (CR), and versus other conventional FRC experiments.

FIG. 2 illustrates the components of the present FRC system and the magnetic topology of an FRC producible in the present FRC system.

FIG. 3A illustrates the basic layout of the present FRC system as viewed from the top, including the preferred arrangement of the central confinement vessel, formation section, divertors, neutral beams, electrodes, plasma guns, mirror plugs and pellet injector.

FIG. 3B illustrates the central confinement vessel as viewed from the top and showing the neutral beams arranged at an angle normal to the major axis of symmetry in the central confinement vessel.

FIG. 3C illustrates the central confinement vessel as viewed from the top and showing the neutral beams arranged at an angle less than normal to the major axis of symmetry in the central confinement vessel and directed to inject particles toward the mid-plane of the central confinement vessel.

FIGS. 3D and 3E illustrate top and perspective views, respectively, of the basic layout of an alternative embodiment of the present FRC system, including the preferred arrangement of the central confinement vessel, formation section, inner and outer divertors, neutral beams arranged at an angle less than normal to the major axis of symmetry in the central confinement vessel, electrodes, plasma guns and mirror plugs.

FIG. 4 illustrates a schematic of the components of a pulsed power system for the formation sections.

FIG. 5 illustrates an isometric view of an individual pulsed power formation skid.

FIG. 6 illustrates an isometric view of a formation tube assembly.

FIG. 7 illustrates a partial sectional isometric view of neutral beam system and key components.

FIG. 8 illustrates an isometric view of the neutral beam arrangement on confinement chamber.

FIG. 9 illustrates a partial sectional isometric view of a preferred arrangement of the Ti and Li gettering systems.

FIG. 10 illustrates a partial sectional isometric view of a plasma gun installed in the divertor chamber. Also shown are the associated magnetic mirror plug and a divertor electrode assembly.

FIG. 11 illustrates a preferred layout of an annular bias electrode at the axial end of the confinement chamber.

FIG. 12 illustrates the evolution of the excluded flux radius in the FRC system obtained from a series of external diamagnetic loops at the two field reversed theta pinch formation sections and magnetic probes embedded inside the central metal confinement chamber. Time is measured from the instant of synchronized field reversal in the formation sources, and distance z is given relative to the axial mid-plane of the machine.

FIGS. 13A, 13B, 13C and 13D illustrate data from a representative non-HPF, un-sustained discharge on the present FRC system. Shown as functions of time are (FIG. 13A) excluded flux radius at the mid-plane, (FIG. 13B) 6 chords of line-integrated density from the mid-plane CO2 interferometer, (FIG. 13C) Abel-inverted density radial profiles from the CO2 interferometer data, and (FIG. 13D) total plasma temperature from pressure balance.

FIG. 14 illustrates the excluded flux axial profiles at selected times for the same discharge of the present FRC system shown in FIGS. 13A, 13B, 13C and 13D.

FIG. 15 illustrates an isometric view of the saddle coils mounted outside of the confinement chamber.

FIGS. 16A, 16B, 16C and 16D illustrate the correlations of FRC lifetime and pulse length of injected neutral beams. As shown, longer beam pulses produce longer lived FRCs.

FIGS. 17A, 17B, 17C and 17D the individual and combined effects of different components of the FRC system on FRC performance and the attainment of the HPF regime.

FIGS. 18 A, 18B, 18C and 18D illustrate data from a representative HPF, un-sustained discharge on the present FRC system. Shown as functions of time are (FIG. 18A) excluded flux radius at the mid-plane, (FIG. 18B) 6 chords of line-integrated density from the mid-plane CO2 interferometer, (FIG. 18C) Abel-inverted density radial profiles from the CO2 interferometer data, and (FIG. 18D) total plasma temperature from pressure balance.

FIG. 19 illustrates flux confinement as a function of electron temperature (T_(e)). It represents a graphical representation of a newly established superior scaling regime for HPF discharges.

FIG. 20 illustrates the FRC lifetime corresponding to the pulse length of non-angled and angled injected neutral beams.

FIGS. 21A, 21B, 21C, 21D and 21E illustrate the pulse length of angled injected neutral beams and the lifetime of FRC plasma parameters of plasma radius, plasma density, plasma temperature, and magnetic flux corresponding to the pulse length of angled injected neutral beams.

FIGS. 22A and 22B illustrate the basic layout of a compact toroid (CT) injector.

FIGS. 23A and 23B illustrate the central confinement vessel showing the CT injector mounted thereto.

FIGS. 24A and 24B illustrate the basic layout of an alternative embodiment of the CT injector having a drift tube coupled thereto.

FIG. 25 illustrates the central confinement vessel as viewed from the top and showing the neutral beams arranged at an angle less than normal to the major axis of symmetry in the central confinement vessel and directed to inject particles toward the mid-plane of the central confinement vessel and showing antennas from which high harmonic fast waves are propagated at an angle less than normal to the major axis of symmetry in the central confinement vessel and directed to propagate from the mid-plane of the central confinement vessel for heating of plasma electrons.

FIGS. 26A and 26B illustrate a complete radial density profile and a complete radial electron temperature profile of an FRC plasma of the present FRC system.

FIGS. 27A-27D illustrate radial profiles of system equilibrium and characteristic frequency at mid-plane (Z=0) of the present FRC system.

FIGS. 28A-28C illustrate observations of power absorption and mode conversion under electron heating conditions of microwave at 8 GHz in an FRC plasma of the present FRC system.

FIGS. 29A-29F illustrate observations of power absorption and mode conversion under electron heating conditions of microwave at 50 GHz in an FRC plasma of the present FRC system.

FIGS. 30A-30C illustrate observations of power absorption under electron heating conditions of whistler wave at 0.5 GHz in an FRC plasma of the present FRC system.

FIG. 31 illustrates a density profile and wave propagation in an FRC plasma of the present FRC system.

FIG. 32 illustrates a poloidal flux profile and wave propagation in an FRC plasma of the present FRC system.

FIG. 33 illustrates an exemplary density profile and wave propagation trajectory in an FRC plasma of the present FRC system.

FIG. 34 illustrates an exemplary ω/ω_(ci[D]) profile and wave propagation trajectory in an FRC plasma of the present FRC system.

FIG. 35 illustrates exemplary power damping with the distance of wave propagation in an FRC plasma of the present FRC system.

FIG. 36 illustrates an exemplary power absorption profile in an FRC plasma of the present FRC system.

FIGS. 37A and 37B illustrate exemplary radial profiles of power density in an FRC plasma of the present FRC system.

FIG. 38 illustrates an exemplary 2D profile of damping power density in an FRC plasma of the present FRC system.

FIG. 39 illustrates an exemplary power damping profile in an FRC plasma of the present FRC system.

FIG. 40 illustrates an exemplary finite-ion-Larmor-radius profile in an FRC plasma of the present FRC system.

FIG. 41 illustrates an exemplary power absorption profile in an FRC plasma of the present FRC system.

FIG. 42 illustrates an exemplary profile of an FRC plasma of the present FRC system.

It should be noted that the figures are not necessarily drawn to scale and that elements of similar structures or functions are generally represented by like reference numerals for illustrative purposes throughout the figures. It also should be noted that the figures are only intended to facilitate the description of the various embodiments described herein. The figures do not necessarily describe every aspect of the teachings disclosed herein and do not limit the scope of the claims.

DETAILED DESCRIPTION

The present embodiments provided herein are directed to systems and methods that facilitate forming and maintaining FRCs with superior stability as well as particle, energy and flux confinement. Some of the present embodiments are directed to systems and methods that facilitate forming and maintaining FRCs with elevated system energies and temperatures and improved sustainment utilizing neutral beam injection and high harmonic fast wave electron heating.

Representative examples of the embodiments described herein, which examples utilize many of these additional features and teachings both separately and in combination, will now be described in further detail with reference to the attached drawings. This detailed description is merely intended to teach a person of skill in the art further details for practicing preferred aspects of the present teachings and is not intended to limit the scope of the invention. Therefore, combinations of features and steps disclosed in the following detail description may not be necessary to practice the invention in the broadest sense, and are instead taught merely to particularly describe representative examples of the present teachings.

Moreover, the various features of the representative examples and the dependent claims may be combined in ways that are not specifically and explicitly enumerated in order to provide additional useful embodiments of the present teachings. In addition, it is expressly noted that all features disclosed in the description and/or the claims are intended to be disclosed separately and independently from each other for the purpose of original disclosure, as well as for the purpose of restricting the claimed subject matter independent of the compositions of the features in the embodiments and/or the claims. It is also expressly noted that all value ranges or indications of groups of entities disclose every possible intermediate value or intermediate entity for the purpose of original disclosure, as well as for the purpose of restricting the claimed subject matter.

Before turning to the systems and methods that facilitate high harmonic fast wave electron heating in FRC plasmas, a discussion of systems and methods for forming and maintaining high performance FRCs with superior stability as well as superior particle, energy and flux confinement over conventional FRCs, as well as a discussion of systems and methods for forming and maintaining high performance FRCs at or about a constant value without decay are provided. Such high performance FRCs provide a pathway to a whole variety of applications including compact neutron sources (for medical isotope production, nuclear waste remediation, materials research, neutron radiography and tomography), compact photon sources (for chemical production and processing), mass separation and enrichment systems, and reactor cores for fusion of light nuclei for the future generation of energy.

Various ancillary systems and operating modes have been explored to assess whether there is a superior confinement regime in FRCs. These efforts have led to breakthrough discoveries and the development of a High Performance FRC paradigm described herein. In accordance with this new paradigm, the present systems and methods combine a host of novel ideas and means to dramatically improve FRC confinement as illustrated in FIG. 1 as well as provide stability control without negative side-effects. As discussed in greater detail below, FIG. 1 depicts particle confinement in an FRC system 10 described below (see FIGS. 2 and 3), operating in accordance with a High Performance FRC regime (HPF) for forming and maintaining an FRC versus operating in accordance with a conventional regime CR for forming and maintaining an FRC, and versus particle confinement in accordance with conventional regimes for forming and maintaining an FRC used in other experiments. The present disclosure will outline and detail the innovative individual components of the FRC system 10 and methods as well as their collective effects.

FRC System

Vacuum System

FIGS. 2 and 3 depict a schematic of the present FRC system 10. The FRC system 10 includes a central confinement vessel 100 surrounded by two diametrically opposed reversed-field-theta-pinch formation sections 200 and, beyond the formation sections 200, two divertor chambers 300 to control neutral density and impurity contamination. The present FRC system 10 was built to accommodate ultrahigh vacuum and operates at typical base pressures of 10⁻⁸ torr. Such vacuum pressures require the use of double-pumped mating flanges between mating components, metal O-rings, high purity interior walls, as well as careful initial surface conditioning of all parts prior to assembly, such as physical and chemical cleaning followed by a 24 hour 250° C. vacuum baking and Hydrogen glow discharge cleaning.

The reversed-field-theta-pinch formation sections 200 are standard field-reversed-theta-pinches (FRTPs), albeit with an advanced pulsed power formation system discussed in detail below (see FIGS. 4 through 6). Each formation section 200 is made of standard opaque industrial grade quartz tubes that feature a 2 millimeter inner lining of ultrapure quartz. The confinement chamber 100 is made of stainless steel to allow a multitude of radial and tangential ports; it also serves as a flux conserver on the timescale of the experiments described below and limits fast magnetic transients. Vacuums are created and maintained within the FRC system 10 with a set of dry scroll roughing pumps, turbo molecular pumps and cryo pumps.

Magnetic System

The magnetic system 400 is illustrated in FIGS. 2 and 3. FIG. 2, amongst other features, illustrates an FRC magnetic flux and density contours (as functions of the radial and axial coordinates) pertaining to an FRC 450 producible by the FRC system 10. These contours were obtained by a 2-D resistive Hall-MHD numerical simulation using code developed to simulate systems and methods corresponding to the FRC system 10, and agree well with measured experimental data. As seen in FIG. 2, the FRC 450 consists of a torus of closed field lines at the interior 453 of the FRC 450 inside a separatrix 451, and of an annular edge layer 456 on the open field lines 452 just outside the separatrix 451. The edge layer 456 coalesces into jets 454 beyond the FRC length, providing a natural divertor.

The main magnetic system 410 includes a series of quasi-dc coils 412, 414, and 416 that are situated at particular axial positions along the components, i.e., along the confinement chamber 100, the formation sections 200 and the divertors 300, of the FRC system 10. The quasi-dc coils 412, 414 and 416 are fed by quasi-dc switching power supplies and produce basic magnetic bias fields of about 0.1 T in the confinement chamber 100, the formation sections 200 and the divertors 300. In addition to the quasi-dc coils 412, 414 and 416, the main magnetic system 410 includes quasi-dc mirror coils 420 (fed by switching supplies) between either end of the confinement chamber 100 and the adjacent formation sections 200. The quasi-dc mirror coils 420 provide magnetic mirror ratios of up to 5 and can be independently energized for equilibrium shaping control. In addition, mirror plugs 440, are positioned between each of the formation sections 200 and divertors 300. The mirror plugs 440 comprise compact quasi-dc mirror coils 430 and mirror plug coils 444. The quasi-dc mirror coils 430 include three coils 432, 434 and 436 (fed by switching supplies) that produce additional guide fields to focus the magnetic flux surfaces 455 towards the small diameter passage 442 passing through the mirror plug coils 444. The mirror plug coils 444, which wrap around the small diameter passage 442 and are fed by LC pulsed power circuitry, produce strong magnetic mirror fields of up to 4 T. The purpose of this entire coil arrangement is to tightly bundle and guide the magnetic flux surfaces 455 and end-streaming plasma jets 454 into the remote chambers 310 of the divertors 300. Finally, a set of saddle-coil “antennas” 460 (see FIG. 15) are located outside the confinement chamber 100, two on each side of the mid-plane, and are fed by dc power supplies. The saddle-coil antennas 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of about 0.01 T for controlling rotational instabilities and/or electron current control. The saddle-coil antennas 460 can flexibly provide magnetic fields that are either symmetric or antisymmetric about the machine's mid-plane, depending on the direction of the applied currents.

Pulsed Power Formation Systems

The pulsed power formation systems 210 operate on a modified theta-pinch principle. There are two systems that each power one of the formation sections 200. FIGS. 4 through 6 illustrate the main building blocks and arrangement of the formation systems 210. The formation system 210 is composed of a modular pulsed power arrangement that consists of individual units (=skids) 220 that each energize a sub-set of coils 232 of a strap assembly 230 (=straps) that wrap around the formation quartz tubes 240. Each skid 220 is composed of capacitors 221, inductors 223, fast high current switches 225 and associated trigger 222 and dump circuitry 224. In total, each formation system 210 stores between 350-400 kJ of capacitive energy, which provides up to 35 GW of power to form and accelerate the FRCs. Coordinated operation of these components is achieved via a state-of-the-art trigger and control system 222 and 224 that allows synchronized timing between the formation systems 210 on each formation section 200 and minimizes switching jitter to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRCs can be formed in-situ and then accelerated and injected (=static formation) or formed and accelerated at the same time (=dynamic formation).

Neutral Beam Injectors

Neutral atom beams 600 are deployed on the FRC system 10 to provide heating and current drive as well as to develop fast particle pressure. As shown in FIGS. 3A, 3B and 8, the individual beam lines comprising neutral atom beam injector systems 610 and 640 are located around the central confinement chamber 100 and inject fast particles tangentially to the FRC plasma (and perpendicular or at an angle normal to the major axis of symmetry in the central confinement vessel 100) with an impact parameter such that the target trapping zone lies well within the separatrix 451 (see FIG. 2). Each injector system 610 and 640 is capable of injecting up to 1 MW of neutral beam power into the FRC plasma with particle energies between 20 and 40 keV. The systems 610 and 640 are based on positive ion multi-aperture extraction sources and utilize geometric focusing, inertial cooling of the ion extraction grids and differential pumping. Apart from using different plasma sources, the systems 610 and 640 are primarily differentiated by their physical design to meet their respective mounting locations, yielding side and top injection capabilities. Typical components of these neutral beam injectors are specifically illustrated in FIG. 7 for the side injector systems 610. As shown in FIG. 7, each individual neutral beam system 610 includes an RF plasma source 612 at an input end (this is substituted with an arc source in systems 640) with a magnetic screen 614 covering the end. An ion optical source and acceleration grids 616 is coupled to the plasma source 612 and a gate valve 620 is positioned between the ion optical source and acceleration grids 616 and a neutralizer 622. A deflection magnet 624 and an ion dump 628 are located between the neutralizer 622 and an aiming device 630 at the exit end. A cooling system comprises two cryo-refrigerators 634, two cryopanels 636 and a LN2 shroud 638. This flexible design allows for operation over a broad range of FRC parameters.

An alternative configuration for the neutral atom beam injectors 600 is that of injecting the fast particles tangentially to the FRC plasma, but with an angle A less than 90° relative to the major axis of symmetry in the central confinement vessel 100. These types of orientation of the beam injectors 615 are shown in FIG. 3C. In addition, the beam injectors 615 may be oriented such that the beam injectors 615 on either side of the mid-plane of the central confinement vessel 100 inject their particles towards the mid-plane. Finally, the axial position of these beam systems 600 may be chosen closer to the mid-plane. These alternative injection embodiments facilitate a more central fueling option, which provides for better coupling of the beams and higher trapping efficiency of the injected fast particles. Furthermore, depending on the angle and axial position, this arrangement of the beam injectors 615 allows more direct and independent control of the axial elongation and other characteristics of the FRC 450. For instance, injecting the beams at a shallow angle A relative to the vessel's major axis of symmetry will create an FRC plasma with longer axial extension and lower temperature while picking a more perpendicular angle A will lead to an axially shorter but hotter plasma. In this fashion the injection angle A and location of the beam injectors 615 can be optimized for different purposes. In addition, such angling and positioning of the beam injectors 615 can allow beams of higher energy (which is generally more favorable for depositing more power with less beam divergence) to be injected into lower magnetic fields than would otherwise be necessary to trap such beams. This is due to the fact that it is the azimuthal component of the energy that determines fast ion orbit scale (which becomes progressively smaller as the injection angle relative to the vessel's major axis of symmetry is reduced at constant beam energy). Furthermore, angled injection towards the mid-plane and with axial beam positions close to the mid-plane improves beam-plasma coupling, even as the FRC plasma shrinks or otherwise axially contracts during the injection period.

Turning to FIGS. 3D and 3E, another alternative configuration of the FRC system 10 includes inner divertors 302 in addition to the angled beam injectors 615. The inner divertors 302 are positioned between the formation sections 200 and the confinement chamber 100, and are configured and operate substantially similar to the outer divertors 300. The inner divertors 302, which include fast switching magnetic coils therein, are effectively inactive during the formation process to enable the formation FRCs to pass through the inner divertors 302 as the formation FRCs translate toward the mid-plane of the confinement chamber 100. Once the formation FRCs pass through the inner divertors 302 into the confinement chamber 100, the inner divertors are activated to operate substantially similar to the outer divertors and isolate the confinement chamber 100 from the formation sections 200.

Pellet Injector

To provide a means to inject new particles and better control FRC particle inventory, a 12-barrel pellet injector 700 (see e.g. I. Vinyar et al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,” Proceedings of the 26th Fusion Science and Technology Symposium, Sep. 27 to Oct. 1 (2010)) is utilized on FRC system 10. FIG. 3 illustrates the layout of the pellet injector 700 on the FRC system 10. The cylindrical pellets (D˜1 mm, L˜1-2 mm) are injected into the FRC with a velocity in the range of 150-250 km/s. Each individual pellet contains about 5×10¹⁹ hydrogen atoms, which is comparable to the FRC particle inventory.

Gettering Systems

It is well known that neutral halo gas is a serious problem in all confinement systems. The charge exchange and recycling (release of cold impurity material from the wall) processes can have a devastating effect on energy and particle confinement. In addition, any significant density of neutral gas at or near the edge will lead to prompt losses of or at least severely curtail the lifetime of injected large orbit (high energy) particles (large orbit refers to particles having orbits on the scale of the FRC topology or at least orbit radii much larger than the characteristic magnetic field gradient length scale)—a fact that is detrimental to all energetic plasma applications, including fusion via auxiliary beam heating.

Surface conditioning is a means by which the detrimental effects of neutral gas and impurities can be controlled or reduced in a confinement system. To this end the FRC system 10 provided herein employs Titanium and Lithium deposition systems 810 and 820 that coat the plasma facing surfaces of the confinement chamber (or vessel) 100 and divertors 300 and 302 with films (tens of micrometers thick) of Ti and/or Li. The coatings are achieved via vapor deposition techniques. Solid Li and/or Ti are evaporated and/or sublimated and sprayed onto nearby surfaces to form the coatings. The sources are atomic ovens with guide nozzles (in case of Li) 822 or heated spheres of solid with guide shrouding (in case of Ti) 812. Li evaporator systems typically operate in a continuous mode while Ti sublimators are mostly operated intermittently in between plasma operation. Operating temperatures of these systems are above 600° C. to obtain fast deposition rates. To achieve good wall coverage, multiple strategically located evaporator/sublimator systems are necessary. FIG. 9 details a preferred arrangement of the gettering deposition systems 810 and 820 in the FRC system 10. The coatings act as gettering surfaces and effectively pump atomic and molecular hydrogenic species (H and D). The coatings also reduce other typical impurities such as Carbon and Oxygen to insignificant levels.

Mirror Plugs

As stated above, the FRC system 10 employs sets of mirror coils 420, 430, and 444 as shown in FIGS. 2 and 3. A first set of mirror coils 420 is located at the two axial ends of the confinement chamber 100 and is independently energized from the DC confinement, formation and divertor coils 412, 414 and 416 of the main magnetic system 410. The first set of mirror coils 420 primarily helps to steer and axially contain the FRC 450 during merging and provides equilibrium shaping control during sustainment. The first mirror coil set 420 produces nominally higher magnetic fields (around 0.4 to 0.5 T) than the central confinement field produced by the central confinement coils 412. The second set of mirror coils 430, which includes three compact quasi-dc mirror coils 432, 434 and 436, is located between the formation sections 200 and the divertors 300 and are driven by a common switching power supply. The mirror coils 432, 434 and 436, together with the more compact pulsed mirror plug coils 444 (fed by a capacitive power supply) and the physical constriction 442 form the mirror plugs 440 that provide a narrow low gas conductance path with very high magnetic fields (between 2 to 4 T with rise times of about 10 to 20 ms). The most compact pulsed mirror coils 444 are of compact radial dimensions, bore of 20 cm and similar length, compared to the meter-plus-scale bore and pancake design of the confinement coils 412, 414 and 416. The purpose of the mirror plugs 440 is multifold: (1) The coils 432, 434, 436 and 444 tightly bundle and guide the magnetic flux surfaces 452 and end-streaming plasma jets 454 into the remote divertor chambers 300. This assures that the exhaust particles reach the divertors 300 appropriately and that there are continuous flux surfaces 455 that trace from the open field line 452 region of the central FRC 450 all the way to the divertors 300. (2) The physical constrictions 442 in the FRC system 10, through which that the coils 432, 434, 436 and 444 enable passage of the magnetic flux surfaces 452 and plasma jets 454, provide an impediment to neutral gas flow from the plasma guns 350 that sit in the divertors 300. In the same vein, the constrictions 442 prevent back-streaming of gas from the formation sections 200 to the divertors 300 thereby reducing the number of neutral particles that has to be introduced into the entire FRC system 10 when commencing the startup of an FRC. (3) The strong axial mirrors produced by the coils 432, 434, 436 and 444 reduce axial particle losses and thereby reduce the parallel particle diffusivity on open field lines.

In the alternative configuration shown in FIGS. 3D and 3E, a set of low profile necking coils 421 are positions between the inner divertors 302 and the formations sections 200.

Axial Plasma Guns

Plasma streams from guns 350 mounted in the divertor chambers 310 of the divertors 300 are intended to improve stability and neutral beam performance. The guns 350 are mounted on axis inside the chamber 310 of the divertors 300 as illustrated in FIGS. 3 and 10 and produce plasma flowing along the open flux lines 452 in the divertor 300 and towards the center of the confinement chamber 100. The guns 350 operate at a high density gas discharge in a washer-stack channel and are designed to generate several kiloamperes of fully ionized plasma for 5 to 10 ms. The guns 350 include a pulsed magnetic coil that matches the output plasma stream with the desired size of the plasma in the confinement chamber 100. The technical parameters of the guns 350 are characterized by a channel having a 5 to 13 cm outer diameter and up to about 10 cm inner diameter and provide a discharge current of 10-15 kA at 400-600 V with a gun-internal magnetic field of between 0.5 to 2.3 T.

The gun plasma streams can penetrate the magnetic fields of the mirror plugs 440 and flow into the formation section 200 and confinement chamber 100. The efficiency of plasma transfer through the mirror plug 440 increases with decreasing distance between the gun 350 and the plug 440 and by making the plug 440 wider and shorter. Under reasonable conditions, the guns 350 can each deliver approximately 10²² protons/s through the 2 to 4 T mirror plugs 440 with high ion and electron temperatures of about 150 to 300 eV and about 40 to 50 eV, respectively. The guns 350 provide significant refueling of the FRC edge layer 456, and an improved overall FRC particle confinement.

To further increase the plasma density, a gas box could be utilized to puff additional gas into the plasma stream from the guns 350. This technique allows a several-fold increase in the injected plasma density. In the FRC system 10, a gas box installed on the divertor 300 side of the mirror plugs 440 improves the refueling of the FRC edge layer 456, formation of the FRC 450, and plasma line-tying.

Given all the adjustment parameters discussed above and also taking into account that operation with just one or both guns is possible, it is readily apparent that a wide spectrum of operating modes is accessible.

Biasing Electrodes

Electrical biasing of open flux surfaces can provide radial potentials that give rise to azimuthal E×B motion that provides a control mechanism, analogous to turning a knob, to control rotation of the open field line plasma as well as the actual FRC core 450 via velocity shear. To accomplish this control, the FRC system 10 employs various electrodes strategically placed in various parts of the machine. FIG. 3 depicts biasing electrodes positioned at preferred locations within the FRC system 10.

In principle, there are 4 classes of electrodes: (1) point electrodes 905 in the confinement chamber 100 that make contact with particular open field lines 452 in the edge of the FRC 450 to provide local charging, (2) annular electrodes 900 between the confinement chamber 100 and the formation sections 200 to charge far-edge flux layers 456 in an azimuthally symmetric fashion, (3) stacks of concentric electrodes 910 in the divertors 300 to charge multiple concentric flux layers 455 (whereby the selection of layers is controllable by adjusting coils 416 to adjust the divertor magnetic field so as to terminate the desired flux layers 456 on the appropriate electrodes 910), and finally (4) the anodes 920 (see FIG. 10) of the plasma guns 350 themselves (which intercept inner open flux surfaces 455 near the separatrix of the FRC 450). FIGS. 10 and 11 show some typical designs for some of these.

In all cases these electrodes are driven by pulsed or dc power sources at voltages up to about 800 V. Depending on electrode size and what flux surfaces are intersected, currents can be drawn in the kilo-ampere range.

Un-Sustained Operation of FRC System—Conventional Regime

The standard plasma formation on the FRC system 10 follows the well-developed reversed-field-theta-pinch technique. A typical process for starting up an FRC commences by driving the quasi-dc coils 412, 414, 416, 420, 432, 434 and 436 to steady state operation. The RFTP pulsed power circuits of the pulsed power formation systems 210 then drive the pulsed fast reversed magnet field coils 232 to create a temporary reversed bias of about −0.05 T in the formation sections 200. At this point a predetermined amount of neutral gas at 9-20 psi is injected into the two formation volumes defined by the quartz-tube chambers 240 of the (north and south) formation sections 200 via a set of azimuthally-oriented puff-vales at flanges located on the outer ends of the formation sections 200. Next a small RF (˜hundreds of kilo-hertz) field is generated from a set of antennas on the surface of the quartz tubes 240 to create pre-ionization in the form of local seed ionization regions within the neutral gas columns. This is followed by applying a theta-ringing modulation on the current driving the pulsed fast reversed magnet field coils 232, which leads to more global pre-ionization of the gas columns. Finally, the main pulsed power banks of the pulsed power formation systems 210 are fired to drive pulsed fast reversed magnet field coils 232 to create a forward-biased field of up to 0.4 T. This step can be time-sequenced such that the forward-biased field is generated uniformly throughout the length of the formation tubes 240 (static formation) or such that a consecutive peristaltic field modulation is achieved along the axis of the formation tubes 240 (dynamic formation).

In this entire formation process, the actual field reversal in the plasma occurs rapidly, within about 5 μs. The multi-gigawatt pulsed power delivered to the forming plasma readily produces hot FRCs which are then ejected from the formation sections 200 via application of either a time-sequenced modulation of the forward magnetic field (magnetic peristalsis) or temporarily increased currents in the last coils of coil sets 232 near the axial outer ends of the formation tubes 210 (forming an axial magnetic field gradient that points axially towards the confinement chamber 100). The two (north and south) formation FRCs so formed and accelerated then expand into the larger diameter confinement chamber 100, where the quasi-dc coils 412 produce a forward-biased field to control radial expansion and provide the equilibrium external magnetic flux.

Once the north and south formation FRCs arrive near the mid-plane of the confinement chamber 100, the FRCs collide. During the collision the axial kinetic energies of the north and south formation FRCs are largely thermalized as the FRCs merge ultimately into a single FRC 450. A large set of plasma diagnostics are available in the confinement chamber 100 to study the equilibria of the FRC 450. Typical operating conditions in the FRC system 10 produce compound FRCs with separatrix radii of about 0.4 m and about 3 m axial extend. Further characteristics are external magnetic fields of about 0.1 T, plasma densities around 5×10¹⁹ m⁻³ and total plasma temperature of up to 1 keV. Without any sustainment, i.e., no heating and/or current drive via neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to about 1 ms, the indigenous characteristic configuration decay time.

Experimental Data of Unsustained Operation—Conventional Regime

FIG. 12 shows a typical time evolution of the excluded flux radius, r_(ΔΦ), which approximates the separatrix radius, r_(s), to illustrate the dynamics of the theta-pinch merging process of the FRC 450. The two (north and south) individual plasmoids are produced simultaneously and then accelerated out of the respective formation sections 200 at a supersonic speed, v_(z)˜250 km/s, and collide near the mid-plane at z=0. During the collision the plasmoids compress axially, followed by a rapid radial and axial expansion, before eventually merging to form an FRC 450. Both radial and axial dynamics of the merging FRC 450 are evidenced by detailed density profile measurements and bolometer-based tomography.

Data from a representative un-sustained discharge of the FRC system 10 are shown as functions of time in FIGS. 13A, 13B, 13C and 13D. The FRC is initiated at t=0. The excluded flux radius at the machine's axial mid-plane is shown in FIG. 13A. This data is obtained from an array of magnetic probes, located just inside the confinement chamber's stainless steel wall, that measure the axial magnetic field. The steel wall is a good flux conserver on the time scales of this discharge.

Line-integrated densities are shown in FIG. 13B, from a 6-chord CO2/He—Ne interferometer located at z=0. Taking into account vertical (y) FRC displacement, as measured by bolometric tomography, Abel inversion yields the density contours of FIG. 13C. After some axial and radial sloshing during the first 0.1 ms, the FRC settles with a hollow density profile. This profile is fairly flat, with substantial density on axis, as required by typical 2-D FRC equilibria.

Total plasma temperature is shown in FIG. 13D, derived from pressure balance and fully consistent with Thomson scattering and spectroscopy measurements.

Analysis from the entire excluded flux array indicates that the shape of the FRC separatrix (approximated by the excluded flux axial profiles) evolves gradually from racetrack to elliptical. This evolution, shown in FIG. 14, is consistent with a gradual magnetic reconnection from two to a single FRC. Indeed, rough estimates suggest that in this particular instant about 10% of the two initial FRC magnetic fluxes reconnects during the collision.

The FRC length shrinks steadily from 3 down to about 1 m during the FRC lifetime. This shrinkage, visible in FIG. 14, suggests that mostly convective energy loss dominates the FRC confinement. As the plasma pressure inside the separatrix decreases faster than the external magnetic pressure, the magnetic field line tension in the end regions compresses the FRC axially, restoring axial and radial equilibrium. For the discharge discussed in FIGS. 13A, 13B, 13C and 13D and 14, the FRC magnetic flux, particle inventory, and thermal energy (about 10 mWb, 7×10¹⁹ particles, and 7 kJ, respectively) decrease by roughly an order of magnitude in the first millisecond, when the FRC equilibrium appears to subside.

Sustained Operation—HPF Regime

The examples in FIGS. 12 to 14 are characteristic of decaying FRCs without any sustainment. However, several techniques are deployed on the FRC system 10 to further improve FRC confinement (inner core and edge layer) to the HPF regime and sustain the configuration.

Neutral Beams

First, fast (H) neutrals are injected perpendicular to B_(z) in beams from the eight neutral beam injectors 600. The beams of fast neutrals are injected from the moment the north and south formation FRCs merge in the confinement chamber 100 into one FRC 450. The fast ions, created primarily by charge exchange, have betatron orbits (with primary radii on the scale of the FRC topology or at least much larger than the characteristic magnetic field gradient length scale) that add to the azimuthal current of the FRC 450. After some fraction of the discharge (after 0.5 to 0.8 ms into the shot), a sufficiently large fast ion population significantly improves the inner FRC's stability and confinement properties (see e.g. M. W. Binderbauer and N. Rostoker, Plasma Phys. 56, part 3, 451 (1996)). Furthermore, from a sustainment perspective, the beams from the neutral beam injectors 600 are also the primary means to drive current and heat the FRC plasma.

In the plasma regime of the FRC system 10, the fast ions slow down primarily on plasma electrons. During the early part of a discharge, typical orbit-averaged slowing-down times of fast ions are 0.3-0.5 ms, which results in significant FRC heating, primarily of electrons. The fast ions make large radial excursions outside of the separatrix because the internal FRC magnetic field is inherently low (about 0.03 T on average for a 0.1 T external axial field). The fast ions would be vulnerable to charge exchange loss, if the neutral gas density were too high outside of the separatrix. Therefore, wall gettering and other techniques (such as the plasma gun 350 and mirror plugs 440 that contribute, amongst other things, to gas control) deployed on the FRC system 10 tend to minimize edge neutrals and enable the required build-up of fast ion current.

Pellet Injection

When a significant fast ion population is built up within the FRC 450, with higher electron temperatures and longer FRC lifetimes, frozen H or D pellets are injected into the FRC 450 from the pellet injector 700 to sustain the FRC particle inventory of the FRC 450. The anticipated ablation timescales are sufficiently short to provide a significant FRC particle source. This rate can also be increased by enlarging the surface area of the injected piece by breaking the individual pellet into smaller fragments while in the barrels or injection tubes of the pellet injector 700 and before entering the confinement chamber 100, a step that can be achieved by increasing the friction between the pellet and the walls of the injection tube by tightening the bend radius of the last segment of the injection tube right before entry into the confinement chamber 100. By virtue of varying the firing sequence and rate of the 12 barrels (injection tubes) as well as the fragmentation, it is possible to tune the pellet injection system 700 to provide just the desired level of particle inventory sustainment. In turn, this helps maintain the internal kinetic pressure in the FRC 450 and sustained operation and lifetime of the FRC 450.

Once the ablated atoms encounter significant plasma in the FRC 450, they become fully ionized. The resultant cold plasma component is then collisionally heated by the indigenous FRC plasma. The energy necessary to maintain a desired FRC temperature is ultimately supplied by the beam injectors 600. In this sense the pellet injectors 700 together with the neutral beam injectors 600 form the system that maintains a steady state and sustains the FRC 450.

CT Injector

As an alternative to the pellet injector, a compact toroid (CT) injector is provided, mainly for fueling field-reversed configuration (FRCs) plasmas. The CT injector 720 comprises a magnetized coaxial plasma-gun (MCPG), which, as shown in FIGS. 22A and 22B, includes coaxial cylindrical inner and outer electrodes 722 and 724, a bias coil positioned internal to the inner electrode 726 and an electrical break 728 on an end opposite the discharge of the CT injector 720. Gas is injected through a gas injection port 730 into a space between the inner and outer electrodes 722 and 724 and a Spheromak-like plasma is generated therefrom by discharge and pushed out from the gun by Lorentz force. As shown in FIGS. 23A and 23B, a pair of CT injectors 720 are coupled to the confinement vessel 100 near and on opposition sides of the mid-plane of the vessel 100 to inject CTs into the central FRC plasma within the confinement vessel 100. The discharge end of the CT injectors 720 are directed towards the mid-plane of the confinement vessel 100 at an angle to the longitudinal axis of the confinement vessel 100 similar to the neutral beam injectors 615.

In an alternative embodiment, the CT injector 720, as shown in FIGS. 24A and 24B, include a drift tube 740 comprising an elongate cylindrical tube coupled to the discharge end of the CT injector 720. As depicted, the drift tube 740 includes drift tube coils 742 positioned about and axially spaced along the tube. A plurality of diagnostic ports 744 are depicted along the length of the tube.

The advantages of the CT injector 720 are: (1) control and adjustability of particle inventory per injected CT; (2) warm plasma is deposited (instead of cryogenic pellets); (3) system can be operated in rep-rate mode so as to allow for continuous fueling; (4) the system can also restore some magnetic flux as the injected CTs carry embedded magnetic field. In an embodiment for experimental use, the inner diameter of an outer electrode is 83.1 mm and the outer diameter of an inner electrode is 54.0 mm. The surface of the inner electrode 722 is preferably coated with tungsten in order to reduce impurities coming out from the electrode 722. As depicted, the bias coil 726 is mounted inside of the inner electrode 722.

In recent experiments a supersonic CT translation speed of up to ˜100 km/s was achieved. Other typical plasma parameters are as follows: electron density˜5×1021 m−3, electron temperature˜30-50 eV, and particle inventory of ˜0.5-1.0×1019. The high kinetic pressure of the CT allows the injected plasma to penetrate deeply into the FRC and deposit the particles inside the separatrix. In recent experiments FRC particle fueling has resulted in ˜10-20% of the FRC particle inventory being provide by the CT injectors successfully demonstrating fueling can readily be carried out without disrupting the FRC plasma.

Saddle Coils

To achieve steady state current drive and maintain the required ion current it is desirable to prevent or significantly reduce electron spin up due to the electron-ion frictional force (resulting from collisional ion electron momentum transfer). The FRC system 10 utilizes an innovative technique to provide electron breaking via an externally applied static magnetic dipole or quadrupole field. This is accomplished via the external saddle coils 460 depicted in FIG. 15. The transverse applied radial magnetic field from the saddle coils 460 induces an axial electric field in the rotating FRC plasma. The resultant axial electron current interacts with the radial magnetic field to produce an azimuthal breaking force on the electrons, F_(θ)=−σV_(eθ)<|B_(r)|²>. For typical conditions in the FRC system 10, the required applied magnetic dipole (or quadrupole) field inside the plasma needs to be only of order 0.001 T to provide adequate electron breaking. The corresponding external field of about 0.015 T is small enough to not cause appreciable fast particle losses or otherwise negatively impact confinement. In fact, the applied magnetic dipole (or quadrupole) field contributes to suppress instabilities. In combination with tangential neutral beam injection and axial plasma injection, the saddle coils 460 provide an additional level of control with regard to current maintenance and stability.

Mirror Plugs

The design of the pulsed coils 444 within the mirror plugs 440 permits the local generation of high magnetic fields (2 to 4 T) with modest (about 100 kJ) capacitive energy. For formation of magnetic fields typical of the present operation of the FRC system 10, all field lines within the formation volume are passing through the constrictions 442 at the mirror plugs 440, as suggested by the magnetic field lines in FIG. 2 and plasma wall contact does not occur. Furthermore, the mirror plugs 440 in tandem with the quasi-dc divertor magnets 416 can be adjusted so to guide the field lines onto the divertor electrodes 910, or flare the field lines in an end cusp configuration (not shown). The latter improves stability and suppresses parallel electron thermal conduction.

The mirror plugs 440 by themselves also contribute to neutral gas control. The mirror plugs 440 permit a better utilization of the deuterium gas puffed in to the quartz tubes during FRC formation, as gas back-streaming into the divertors 300 is significantly reduced by the small gas conductance of the plugs (a meager 500 L/s). Most of the residual puffed gas inside the formation tubes 210 is quickly ionized. In addition, the high-density plasma flowing through the mirror plugs 440 provides efficient neutral ionization hence an effective gas barrier. As a result, most of the neutrals recycled in the divertors 300 from the FRC edge layer 456 do not return to the confinement chamber 100. In addition, the neutrals associated with the operation of the plasma guns 350 (as discussed below) will be mostly confined to the divertors 300.

Finally, the mirror plugs 440 tend to improve the FRC edge layer confinement. With mirror ratios (plug/confinement magnetic fields) in the range 20 to 40, and with a 15 m length between the north and south mirror plugs 440, the edge layer particle confinement time τ_(∥) increases by up to an order of magnitude. Improving β_(|) readily increases the FRC particle confinement.

Assuming radial diffusive (D) particle loss from the separatrix volume 453 balanced by axial loss (τ_(∥)) from the edge layer 456, one obtains (2πr_(s)L_(s))(Dn_(s)/δ)=(2πr_(s)L_(s)δ)(n_(s)/τ_(∥)), from which the separatrix density gradient length can be rewritten as δ=(Dτ_(|))^(1/2). Here r_(s), L_(s) and n_(s) are separatrix radius, separatrix length and separatrix density, respectively. The FRC particle confinement time is τ_(N)=[πr_(s) ²L_(s)<n>]/[(2πr_(s)L_(s))(Dn_(s)/δ)]=(<n>/n_(s))(τ_(⊥)τ_(|))^(1/2), where τ_(⊥)a²/D with a=r_(s)/4. Physically, improving τ_(∥) leads to increased δ (reduced separatrix density gradient and drift parameter), and, therefore, reduced FRC particle loss. The overall improvement in FRC particle confinement is generally somewhat less than quadratic because n_(s) increases with τ_(|).

A significant improvement in τ_(∥) also requires that the edge layer 456 remains grossly stable (i.e., no n=1 flute, firehose, or other MHD instability typical of open systems). Use of the plasma guns 350 provides for this preferred edge stability. In this sense, the mirror plugs 440 and plasma gun 350 form an effective edge control system.

Plasma Guns

The plasma guns 350 improve the stability of the FRC exhaust jets 454 by line-tying. The gun plasmas from the plasma guns 350 are generated without azimuthal angular momentum, which proves useful in controlling FRC rotational instabilities. As such the guns 350 are an effective means to control FRC stability without the need for the older quadrupole stabilization technique. As a result, the plasma guns 350 make it possible to take advantage of the beneficial effects of fast particles or access the advanced hybrid kinetic FRC regime as outlined in this disclosure. Therefore, the plasma guns 350 enable the FRC system 10 to be operated with saddle coil currents just adequate for electron breaking but below the threshold that would cause FRC instability and/or lead to dramatic fast particle diffusion.

As mentioned in the Mirror Plug discussion above, if τ_(∥) can be significantly improved, the supplied gun plasma would be comparable to the edge layer particle loss rate (˜10²²/s). The lifetime of the gun-produced plasma in the FRC system 10 is in the millisecond range. Indeed, consider the gun plasma with density n_(e)˜10¹³ cm⁻³ and ion temperature of about 200 eV, confined between the end mirror plugs 440. The trap length L and mirror ratio R are about 15 m and 20, respectively. The ion mean free path due to Coulomb collisions is λ_(ii) 6×10³ cm and, since λ_(ii)lnR/R<L, the ions are confined in the gas-dynamic regime. The plasma confinement time in this regime is τ_(gd)˜RL/2V_(s)˜2 ms, where V_(s) is the ion sound speed. For comparison, the classical ion confinement time for these plasma parameters would be τ_(c)˜0.5τ_(ii)+(lnR)^(0.5))˜0.7 ms. The anomalous transverse diffusion may, in principle, shorten the plasma confinement time. However, in the FRC system 10, if we assume the Bohm diffusion rate, the estimated transverse confinement time for the gun plasma is τ_(⊥)>τ_(gd)˜2 ms. Hence, the guns would provide significant refueling of the FRC edge layer 456, and an improved overall FRC particle confinement.

Furthermore, the gun plasma streams can be turned on in about 150 to 200 microseconds, which permits use in FRC start-up, translation, and merging into the confinement chamber 100. If turned on around t˜0 (FRC main bank initiation), the gun plasmas help to sustain the present dynamically formed and merged FRC 450. The combined particle inventories from the formation FRCs and from the guns is adequate for neutral beam capture, plasma heating, and long sustainment. If turned on at tin the range −1 to 0 ms, the gun plasmas can fill the quartz tubes 210 with plasma or ionize the gas puffed into the quartz tubes, thus permitting FRC formation with reduced or even perhaps zero puffed gas. The latter may require sufficiently cold formation plasma to permit fast diffusion of the reversed bias magnetic field. If turned on at t<−2 ms, the plasma streams could fill the about 1 to 3 m³ field line volume of the formation and confinement regions of the formation sections 200 and confinement chamber 100 with a target plasma density of a few 10¹³ cm⁻³, sufficient to allow neutral beam build-up prior to FRC arrival. The formation FRCs could then be formed and translated into the resulting confinement vessel plasma. In this way the plasma guns 350 enable a wide variety of operating conditions and parameter regimes.

Electrical Biasing

Control of the radial electric field profile in the edge layer 456 is beneficial in various ways to FRC stability and confinement. By virtue of the innovative biasing components deployed in the FRC system 10 it is possible to apply a variety of deliberate distributions of electric potentials to a group of open flux surfaces throughout the machine from areas well outside the central confinement region in the confinement chamber 100. In this way radial electric fields can be generated across the edge layer 456 just outside of the FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and effect its confinement via E×B velocity shear. Any differential rotation between the edge layer 456 and the FRC core 453 can then be transmitted to the inside of the FRC plasma by shear. As a result, controlling the edge layer 456 directly impacts the FRC core 453. Furthermore, since the free energy in the plasma rotation can also be responsible for instabilities, this technique provides a direct means to control the onset and growth of instabilities. In the FRC system 10, appropriate edge biasing provides an effective control of open field line transport and rotation as well as FRC core rotation. The location and shape of the various provided electrodes 900, 905, 910 and 920 allows for control of different groups of flux surfaces 455 and at different and independent potentials. In this way a wide array of different electric field configurations and strengths can be realized, each with different characteristic impact on plasma performance.

A key advantage of all these innovative biasing techniques is the fact that core and edge plasma behavior can be affected from well outside the FRC plasma, i.e. there is no need to bring any physical components in touch with the central hot plasma (which would have severe implications for energy, flux and particle losses). This has a major beneficial impact on performance and all potential applications of the HPF concept.

Experimental Data—HPF Operation

Injection of fast particles via beams from the neutral beam guns 600 plays an important role in enabling the HPF regime. FIGS. 16A, 16B, 16C and 16D illustrate this fact. Depicted is a set of curves showing how the FRC lifetime correlates with the length of the beam pulses. All other operating conditions are held constant for all discharges comprising this study. The data is averaged over many shots and, therefore, represents typical behavior. It is clearly evident that longer beam duration produces longer lived FRCs. Looking at this evidence as well as other diagnostics during this study, it demonstrates that beams increase stability and reduce losses. The correlation between beam pulse length and FRC lifetime is not perfect as beam trapping becomes inefficient below a certain plasma size, i.e., as the FRC 450 shrinks in physical size not all of the injected beams are intercepted and trapped. Shrinkage of the FRC is primarily due to the fact that net energy loss (˜4 MW about midway through the discharge) from the FRC plasma during the discharge is somewhat larger than the total power fed into the FRC via the neutral beams (˜2.5 MW) for the particular experimental setup. Locating the beams at a location closer to the mid-plane of the vessel 100 would tend to reduce these losses and extend FRC lifetime.

FIGS. 17A, 17B, 17C and 17D illustrate the effects of different components to achieve the HPF regime. It shows a family of typical curves depicting the lifetime of the FRC 450 as a function of time. In all cases a constant, modest amount of beam power (about 2.5 MW) is injected for the full duration of each discharge. Each curve is representative of a different combination of components. For example, operating the FRC system 10 without any mirror plugs 440, plasma guns 350 or gettering from the gettering systems 800 results in rapid onset of rotational instability and loss of the FRC topology. Adding only the mirror plugs 440 delays the onset of instabilities and increases confinement. Utilizing the combination of mirror plugs 440 and a plasma gun 350 further reduces instabilities and increases FRC lifetime. Finally adding gettering (Ti in this case) on top of the gun 350 and plugs 440 yields the best results—the resultant FRC is free of instabilities and exhibits the longest lifetime. It is clear from this experimental demonstration that the full combination of components produces the best effect and provides the beams with the best target conditions.

As shown in FIG. 1, the newly discovered HPF regime exhibits dramatically improved transport behavior. FIG. 1 illustrates the change in particle confinement time in the FRC system 10 between the conventionally regime and the HPF regime. As can be seen, it has improved by well over a factor of 5 in the HPF regime. In addition, FIG. 1 details the particle confinement time in the FRC system 10 relative to the particle confinement time in prior conventional FRC experiments. With regard to these other machines, the HPF regime of the FRC system 10 has improved confinement by a factor of between 5 and close to 20. Finally, and most importantly, the nature of the confinement scaling of the FRC system 10 in the HPF regime is dramatically different from all prior measurements. Before the establishment of the HPF regime in the FRC system 10, various empirical scaling laws were derived from data to predict confinement times in prior FRC experiments. All those scaling rules depend mostly on the ratio R²/ρ_(i), where R is the radius of the magnetic field null (a loose measure of the physical scale of the machine) and ρi is the ion larmor radius evaluated in the externally applied field (a loose measure of the applied magnetic field). It is clear from FIG. 1 that long confinement in conventional FRCs is only possible at large machine size and/or high magnetic field. Operating the FRC system 10 in the conventional FRC regime CR tends to follow those scaling rules, as indicated in FIG. 1. However, the HPF regime is vastly superior and shows that much better confinement is attainable without large machine size or high magnetic fields. More importantly, it is also clear from FIG. 1 that the HPF regime results in improved confinement time with reduced plasma size as compared to the CR regime. Similar trends are also visible for flux and energy confinement times, as described below, which have increased by over a factor of 3-8 in the FRC system 10 as well. The breakthrough of the HPF regime, therefore, enables the use of modest beam power, lower magnetic fields and smaller size to sustain and maintain FRC equilibria in the FRC system 10 and future higher energy machines. Hand-in-hand with these improvements comes lower operating and construction costs as well as reduced engineering complexity.

For further comparison, FIGS. 18A, 18B, 18C and 18D show data from a representative HPF regime discharge in the FRC system 10 as a function of time. FIG. 18A depicts the excluded flux radius at the mid-plane. For these longer timescales the conducting steel wall is no longer as good a flux conserver and the magnetic probes internal to the wall are augmented with probes outside the wall to properly account for magnetic flux diffusion through the steel. Compared to typical performance in the conventional regime CR, as shown in FIGS. 13A, 13B, 13C and 13D, the HPF regime operating mode exhibits over 400% longer lifetime.

A representative cord of the line integrated density trace is shown in FIG. 18B with its Abel inverted complement, the density contours, in FIG. 18C. Compared to the conventional FRC regime CR, as shown in FIGS. 13A, 13B, 13C and 13D, the plasma is more quiescent throughout the pulse, indicative of very stable operation. The peak density is also slightly lower in HPF shots—this is a consequence of the hotter total plasma temperature (up to a factor of 2) as shown in FIG. 18D.

For the respective discharge illustrated in FIGS. 18A, 18B, 18C and 18D, the energy, particle and flux confinement times are 0.5 ms, 1 ms and 1 ms, respectively. At a reference time of 1 ms into the discharge, the stored plasma energy is 2 kJ while the losses are about 4 MW, making this target very suitable for neutral beam sustainment.

FIG. 19 summarizes all advantages of the HPF regime in the form of a newly established experimental HPF flux confinement scaling. As can be seen in FIG. 19, based on measurements taken before and after t=0.5 ms, i.e., t≤0.5 ms and t>0.5 ms, the flux confinement (and similarly, particle confinement and energy confinement) scales with roughly the square of the electron Temperature (T_(e)) for a given separatrix radius (r_(s)). This strong scaling with a positive power of T_(e) (and not a negative power) is completely opposite to that exhibited by conventional tokomaks, where confinement is typically inversely proportional to some power of the electron temperature. The manifestation of this scaling is a direct consequence of the HPF state and the large orbit (i.e. orbits on the scale of the FRC topology and/or at least the characteristic magnetic field gradient length scale) ion population. Fundamentally, this new scaling substantially favors high operating temperatures and enables relatively modest sized reactors.

With the advantages the HPF regime presents, FRC sustainment or steady state driven by neutral beams is achievable, meaning global plasma parameters such as plasma thermal energy, total particle numbers, plasma radius and length as well as magnetic flux are sustainable at reasonable levels without substantial decay. For comparison, FIG. 20 shows data in plot A from a representative HPF regime discharge in the FRC system 10 as a function of time and in plot B for a projected representative HPF regime discharge in the FRC system 10 as a function of time where the FRC 450 is sustained without decay through the duration of the neutral beam pulse. For plot A, neutral beams with total power in the range of about 2.5-2.9 MW were injected into the FRC 450 for an active beam pulse length of about 6 ms. The plasma diamagnetic lifetime depicted in plot A was about 5.2 ms. More recent data shows a plasma diamagnetic lifetime of about 7.2 ms is achievable with an active beam pulse length of about 7 ms.

As noted above with regard to FIGS. 16A, 16B, 16C and 16D, the correlation between beam pulse length and FRC lifetime is not perfect as beam trapping becomes inefficient below a certain plasma size, i.e., as the FRC 450 shrinks in physical size not all of the injected beams are intercepted and trapped. Shrinkage or decay of the FRC is primarily due to the fact that net energy loss (−4 MW about midway through the discharge) from the FRC plasma during the discharge is somewhat larger than the total power fed into the FRC via the neutral beams (−2.5 MW) for the particular experimental setup. As noted with regard to FIG. 3C, angled beam injection from the neutral beam guns 600 towards the mid-plane improves beam-plasma coupling, even as the FRC plasma shrinks or otherwise axially contracts during the injection period. In addition, appropriate pellet fueling will maintain the requisite plasma density.

Plot B is the result of simulations run using an active beam pulse length of about 6 ms and total beam power from the neutral beam guns 600 of slightly more than about 10 MW, where neutral beams shall inject H (or D) neutrals with particle energy of about 15 keV. The equivalent current injected by each of the beams is about 110 A. For plot B, the beam injection angle to the device axis was about 20° less than normal with a target radius of 0.19 m. Injection angle can be changed within the range 15°-25° less than normal. The beams are to be injected in the co-current direction azimuthally. The net side force as well as net axial force from the neutral beam momentum injection shall be minimized. As with plot A, fast (H) neutrals are injected from the neutral beam injectors 600 from the moment the north and south formation FRCs merge in the confinement chamber 100 into one FRC 450.

The simulations that where the foundation for plot B use multi-dimensional hall-MHD solvers for the background plasma and equilibrium, fully kinetic Monte-Carlo based solvers for the energetic beam components and all scattering processes, as well as a host of coupled transport equations for all plasma species to model interactive loss processes. The transport components are empirically calibrated and extensively benchmarked against an experimental database.

As shown by plot B, the steady state diamagnetic lifetime of the FRC 450 will be the length of the beam pulse. However, it is important to note that the key correlation plot B shows is that when the beams are turned off the plasma or FRC begins to decay at that time, but not before. The decay will be similar to that which is observed in discharges which are not beam-assisted—probably on order of 1 ms beyond the beam turn off time—and is simply a reflection of the characteristic decay time of the plasma driven by the intrinsic loss processes.

Turning to FIGS. 21A, 21B, 21C, 21D and 21E, experiment results illustrated in the figures indicate achievement of FRC sustainment or steady state driven by angled neutral beams, i.e., global plasma parameters such as plasma radius, plasma density, plasma temperature as well as magnetic flux are sustainable at constant levels without decay in correlation with NB pulse duration. For example, such plasma parameters are essentially being kept constant for ˜5+ms. Such plasma performance, including the sustainment feature, has a strong correlation NB pulse duration, with diamagnetism persisting even several milliseconds after NB termination due to the accumulated fast ions. As illustrated, the plasma performance is only limited by the pulse-length constraints arising from finite stored energies in the associated power supplies of many critical systems, such as the NB injectors as well as other system components.

High Harmonic Fast Wave Electron Heating

As noted above with regard to FIGS. 3A, 3B, 3C, 3D, 3E and 8, the neutral atom beams 600 are deployed on the FRC system 10 to provide heating and current drive as well as to develop fast particle pressure. The individual beam lines comprising neutral atom beam injector systems 600 are located around the central confinement chamber 100 and, as shown in FIGS. 3C, 3D and 3E, are preferably angled to inject neutral particles towards the mid-plane of the confinement chamber 100. To improve FRC sustainment and demonstrate FRC ramp-up to high plasma temperatures and elevated system energies, the present FRC system 10 includes a neutral beam injector (NBI) system 600 of elevated power and expanded pulse length, e.g., for exemplary purposes only, power of about 20+MW with up to 30 ms pulse length.

Neutral beam injection, however, tends to have poor electron heating efficiency due to the mechanism of power damping on electrons through ion-electron collision. The unique characteristics of an FRC plasma of the present FRC system 10, for example, the plasma being unusually over-dense (ω_(pe)>30 ω_(ce) inside the separatrix) and the magnetic field dropping quickly to zero in the plasma core, make it extremely challenging to heat electrons in the core of FRC plasmas. Conventional electron heating scenarios such as electron cyclotron resonant frequency (or its second or third harmonics) heating which is widely utilized in tokamaks, stellarators, and mirror machines, cannot be adapted to FRC plasmas due to the issue of poor wave accessibility into the plasma core. Other electron heating scenarios, such as electron Bernstein waves, upper-hybrid resonant waves, and whistler waves, encounter similar problems or have low heating efficiency when they are applied to FRC plasmas.

In an exemplary embodiment, the present FRC system 10 includes high harmonic fast wave electron heating to elevate plasma electron temperatures and, thus, further improve FRC sustainment. As shown in FIG. 25, the present FRC system 10 includes one or more antennas 650, such as, e.g., a phased array antenna with four (4) strap, deployed on the FRC system 10 and configured to propagate high harmonic fast waves in radio frequency ranges into the FRC plasma in the confinement vessel 100 to provide electron heating in the core of the FRC plasma from about 150 eV to above about 1 keV. In an exemplary embodiment, the antennas 650 would comprise about a 2 MW RF system at about 15-25 Mhz. Heating of electrons via high harmonic fast waves in radio frequency ranges advantageously reduces fast ions charge-exchange loss and improves plasma confinement, as well as enhances plasma current drive efficiency, which goes up with electron temperature Te.

Simulations of electron heating in high performance FRC plasmas such as the FRC plasma of the present FRC system 10 were performed in the following scenarios: (1) upper-hybrid resonant frequency (50 GHz); (2) electron cyclotron resonant (ECR) frequency (28 GHz); (3) electron Bernstein waves (EBW) at frequency of 2.45 GHz, 5 GHz, 8 GHz, and 18 GHz; (4) whistler waves at 0.5 GHz; (5) HHFW at 15 MHz Simulation results have shown clearly that the regime of HHFW not only has extremely strong single pass power absorption (˜100%), but also has very good wave accessibility into the core of FRC plasmas. These simulations indicated that the conflict between good wave accessibility and efficient power damping on electrons is solved by using this high harmonic fast wave (HHFW) heating, which has been successfully adapted to high beta, over dense spherical tokamak (ST) plasmas such as NSTX for the experiments of core electron heating and off-axis current drive.

The heating mechanism of HHFW includes both electron Landau damping (LD) (where the force acting on electrons is F_(LD)=eE_(//)) and transit time magnetic pumping (TTMP or MP) (in which the force is F_(MP)=−∇_(//)(μB_(//))). Here e and μ are electron's charge and magnetic moment, and E_(//) and B_(//) are the parallel components of the fast wave electric and magnetic field, respectively. Conventional fast wave electron heating in tokamak plasmas requires wave parallel phase velocity V_(ph//)≡ω/k_(//)˜V_(Te) electron thermal velocity) for any significant absorption via dominated LD; MP makes no significant contribution to electron damping and often it can be neglected. Moreover, the absorption of fast wave in tokamak plasmas is weak and therefore it is usually required to have a strong electron preheating by microwaves at electron cyclotron resonant frequency in order to enhance multiple-pass power absorption. However, in high beta, ST plasmas like NSTX, it was found that the MP significantly increases power absorption on electrons over the electron LD alone, and it becomes substantially large at a higher range of phase velocity, ω/k_(//)≤2.5 V_(Te). The combination of MP and LD can lead to 100% single pass absorption.

In high beta regimes such as high performance FRC plasma of the present FRC system 10 (which has the value of β_(e) around 90% in core plasma), damping is dominated by magnetic pumping, which can be scaled as Im k_(⊥)∝n_(e)T_(e)/B²∝β_(e),

and magnetic pumping becomes significant when ω/k_(//)≤2.5 V_(Te). In simulations for the present FRC system 10, T_(e)=150 eV, T_(i)=800 eV, n_(e)=n_(i)=3.2×10¹⁹ m⁻³, magnetic field B=1000 Gauss, HHFW has 1 MW launched power and its frequency is selected as f=15 MHz, thus ω=2πf=10 ω_(ci)[H]=20 ω_(ci) [D]<<ω_(LH), single pass absorption larger than 99% was achieved, and the HHFW power damped on electrons were shown to be as high as 90%. Power damped on ions or damped through collision, can be less than 5% respectively. Moreover, radial profiles of power deposition on electrons, ions and through collision have shown more than 60% of HHFW power is damped inside the separatrix layer of FRC plasmas.

FIGS. 26A and 26B illustrate a complete radial density profile and a complete radial electron temperature profile of an FRC plasma of the present FRC system 10. The present FRC system, according to embodiments of the present disclosure, is configured according to the parameter and value pairs shown in Table 1.

TABLE 1 Parameters for the present FRC system Parameter Value B_(ext), kG ~1 r_(s), cm ~36 L, m 2-3 N_(e), cm−3 ~3 × 10¹³ T_(i), eV 500-800 T_(e), eV 100-150

FIGS. 27A-27D illustrate radial profiles of C-2U equilibrium and characteristic frequency at mid-plane (Z=0) of the present FRC system 10. Challenges observed are that, inside the separatrix layer, plasma is over dense (ω_(pe)>30 ω_(ee)) and B drops quickly to 0 within 11 cm radial distance. All ECR harmonic resonant layers are compacted in a very narrow region thus microwaves can propagate radially only for a very short distance.

The following simulations were conducted with GENRAY-C ray-tracing code for the scenarios in microwave frequency as follows:

EBW (2.45 GHz, 5 GHz, 8 GHz, 18 GHz, and 28 GHz);

Upper-hybrid resonant frequency (50 GHz, 55 GHz);

Whistler wave frequency (0.5-1.0 GHz).

Unfortunately, these scenarios cannot solve the conflict between wave penetration into plasma core and efficient power damping on electrons.

FIGS. 28A-28C illustrate observations of power absorption and mode conversion under Electron Bernstein wave (EBW) electron heating conditions of microwave at 8 GHz in an FRC plasma of the present FRC system 10. In FIGS. 28A-28C, six rays are launched at different angles, a clear O→X→B conversion is observed. More than 90% microwave power can be absorbed by electrons at the 4^(th) harmonic ECR layer (outside separatrix); which results in very localized absorption. The EBW regime can only heat electrons at plasma edge, it cannot penetrate into plasma core.

FIGS. 29A-29F illustrate observations of power absorption and mode conversion under electron heating conditions of microwave at 50 GHz in an FRC plasma of the present FRC system 10. In FIGS. 29A-29F, it is observed that rays stop propagating after O→X→B conversion, and that 30% of microwave power is absorbed.

FIGS. 30A-30C illustrate observations of power absorption under electron heating conditions of whistler wave at 0.5 GHz in an FRC plasma of the present FRC system 10. In FIGS. 30A-30C, it is observed that whistler wave at 0.5 GHz (˜¼fce) has high power absorption but poor wave accessibility. A wave is launched with a large N_(//) (starting at 16) and the wave turns around when there is a large curvature of magnetic field.

In contrast to these heating regimes, high harmonic fast wave heating provides, as demonstrated by simulation results, the following for FRC plasma with high average β_(e)(≈90%) such as an FRC plasma of the present FRC system 10: 1) strong single pass absorption (≈100%); 2) good accessibility to plasma core; 3) efficient power absorption by core electrons of up to 60%; 4) power damping on electrons is dominated by magnetic pumping (TTMP), which can be scaled as lm k_(⊥)∝n_(e)T_(e)/B²∝β_(e).

FIG. 31 illustrates a density profile and wave propagation in an FRC plasma of the present FRC system 10. In FIG. 10, T_(e)=150 eV, while T_(e) (separatrix)=100 eV. T_(i)=800 eV, while T_(i) (separatrix)=200 eV. Thermal ions have the same density and profile as electrons. Fast ions information is not included in FIG. 31. FIG. 32 illustrates a poloidal flux profile and wave propagation in an FRC plasma of the present FRC system 10.

FIG. 33 illustrates an exemplary density profile and wave propagation trajectory in an FRC plasma of the present FRC system 10. In FIG. 33, T_(e)=150 eV, while T_(e) (separatrix)=100 eV. T_(i)=800 eV, while T_(i) (separatrix)=200 eV. In FIG. 33, f=6 MHz (initial ω/ω_(ci[D])˜9), with 1 MW total power. Five rays are launched at mid-plane with initial n_(//) between 4 and 6.

FIG. 34 illustrates an exemplary ω/ω_(ci[D]) profile and wave propagation trajectory in an FRC plasma of the present FRC system 10. In FIG. 34, levels of ω/ω_(ci[D])>28 are not displayed for clarity. The dotted lines in the gap are magnetic flux contour.

FIG. 35 illustrates exemplary power damping with the distance of wave propagation in an FRC plasma of the present FRC system 10. In FIG. 35, five rays are included with different n_(//) between 4 and 6. Each ray has 200 KW power at launching point. The region of significant power damping is between 30 cm and 50 cm.

FIG. 36 illustrates an exemplary power absorption profile in an FRC plasma of the present FRC system 10. In FIG. 36, there is observed significant power absorption on ions and electrons when HHFWs penetrate through the separatrix layer.

FIGS. 37A and 37B illustrate exemplary radial profiles of power density in an FRC plasma of the present FRC system 10. The radial profiles of power density are for (a) total absorption, (b) damping on electrons, (c) damping on ions, and (d) collisional damping. In FIG. 37A, P_(total)=1000 kW, P_(e)=448 kW, P_(i)=486 kW, and P_(cl)=66 kW. In FIG. 37B, P_(total)=999 kW, P_(e)=720 kW, P_(i)=194 kW, and P_(cl)=85 kW. A single pass absorption of 100% is observed during HHFW heating in plasma core.

FIG. 38 illustrates an exemplary 2D profile of damping power density in an FRC plasma of the present FRC system 10.

FIG. 39 illustrates an exemplary power damping profile in an FRC plasma of the present FRC system 10. In FIG. 39, it is observed that the power damping on electrons increases to a maximum when |B| approaches to a minimum. There is observed a very small |E_(//)/E| thus less effect of Landau damping on power absorption.

FIG. 40 illustrates an exemplary finite-ion-Larmor-radius profile in an FRC plasma of the present FRC system 10. In FIG. 40, significant finite-ion-Larmor-radius effects are observed even when the ion temperature T_(i)<1 keV. Inside the separatrix, K_(⊥)×ρ_(Larmor)>>1. It goes to infinity at field null in mid-plane (z=0). This can lead to thermal ions interaction with HHFW thus power damping on thermal ions.

FIG. 41 illustrates an exemplary power absorption profile in an FRC plasma of the present FRC system 10. In FIG. 41, significant power absorption by thermal ions is observed. Ion cyclotron resonant absorption is observed with harmonics number n=(11-20). Conditions for significant power damping on ions are K_(⊥)×ρ_(Larmor)>>1 and ω/K_(⊥)<2V_(Ti).

FIG. 42 illustrates an exemplary profile in an FRC plasma of the present FRC system 10. In FIG. 42, changes of (a) local |B(r,z)|, (b) imaginary part of perpendicular wave number K_(i), (c) ratio of |E_(\\)/E|, and (d) parallel refractive index n_(//) are observed with the distance along the wave propagation.

Simulations of HHFW heating of an FRC plasma of the present FRC system 10 have clearly demonstrated that HHFW heating results in: 1) 100% single pass power absorption; 2) TTMP being dominated power absorption mechanism for core electron heating; 3) maximum power damping on electrons occurring when wave parallel phase velocity V_(ph//)=ω/k_(//)<V_(Te); and, 4) significant power absorption by thermal ions tending to happen when the conditions of K_(⊥)×ρ_(Larm)>>1 and ω/k_(⊥)<2 V_(Ti) are held.

According to an embodiment of the present disclosure, a method for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising forming an FRC about a plasma in a confinement chamber, injecting a plurality of neutral beams into the FRC plasma at an angle toward the mid-plane of the confinement chamber, and heating electrons of the FRC plasma with high harmonic fast waves propagating into the FRC plasma.

According to a further embodiment of the present disclosure, heating electrons includes launching a plurality of high harmonic fast waves from one or more antennas into the FRC plasma in the confinement chamber.

According to a further embodiment of the present disclosure, heating electrons includes launching a plurality of high harmonic fast waves from one or more antennas into the FRC plasma in the confinement chamber at a launch angle from the mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, the launch angle is in a range of about 15° to about 25° from the mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, the launch angle is near but less than normal to a longitudinal axis of the confinement chamber.

According to a further embodiment of the present disclosure, the one or more antennas is a phased array antenna with a plurality of straps.

According to a further embodiment of the present disclosure, the high harmonic fast waves are fast waves in radio frequency ranges.

According to a further embodiment of the present disclosure, heating the electrons including heating the electrons from about 150 eV to above about 1 keV.

According to a further embodiment of the present disclosure, the method further includes maintaining the FRC at or about a constant value without decay and elevating the plasma electron temperature to above about 1.0 keV.

According to a further embodiment of the present disclosure, the method further comprising generating a magnetic field within the confinement chamber with quasi dc coils extending about the confinement chamber and a mirror magnetic field within opposing ends of the confinement chamber with quasi dc mirror coils extending about the opposing ends of the confinement chamber.

According to a further embodiment of the present disclosure, the method further comprising generating a magnetic field within the confinement chamber with quasi dc coils extending about the confinement chamber and a mirror magnetic field within opposing ends of the confinement chamber with quasi dc mirror coils extending about the opposing ends of the confinement chamber.

According to a further embodiment of the present disclosure, forming the FRC includes forming a formation FRC in opposing first and second formation sections coupled to the confinement chamber and accelerating the formation FRC from the first and second formation sections towards the mid through plane of the confinement chamber where the two formation FRCs merge to form the FRC.

According to a further embodiment of the present disclosure, forming the FRC includes one of forming a formation FRC while accelerating the formation FRC towards the mid-plane of the confinement chamber and forming a formation FRC then accelerating the formation FRC towards the mid through plane of the confinement chamber.

According to a further embodiment of the present disclosure, accelerating the formation FRC from the first and second formation sections towards the mid-plane of the confinement chamber includes passing the formation FRC from the first and second formation sections through first and second inner divertors coupled to opposite ends of the confinement chamber interposing the confinement chamber and the first and second formation sections.

According to a further embodiment of the present disclosure, passing the formation FRC from the first and second formation sections through first and second inner divertors includes inactivating the first and second inner divertors as the formation FRC from the first and second formation sections passes through the first and second inner divertors.

According to a further embodiment of the present disclosure, the method further comprising guiding magnetic flux surfaces of the FRC into the first and second inner divertors.

According to a further embodiment of the present disclosure, the method further comprising guiding magnetic flux surfaces of the FRC into first and second outer divertors coupled to the ends of the formation sections.

According to a further embodiment of the present disclosure, the method further comprising generating a magnetic field within the formation sections and the first and second outer divertors with quasi-dc coils extending about the formation sections and divertors.

According to a further embodiment of the present disclosure, the method further comprising generating a magnetic field within the formation sections and first and second inner divertors with quasi-dc coils extending about the formation sections and divertors.

According to a further embodiment of the present disclosure, the method further comprising generating a mirror magnetic field between the first and second formation sections and the first and second outer divertors with quasi-dc mirror coils.

According to a further embodiment of the present disclosure, the method further comprising generating a mirror plug magnetic field within a constriction between the first and second formation sections and the first and second outer divertors with quasi-dc mirror plug coils extending about the constriction between the formation sections and the divertors.

According to a further embodiment of the present disclosure, the method further comprising generating a mirror magnetic field between the confinement chamber and the first and second inner divertors with quasi-dc mirror coils and generating a necking magnetic field between the first and second formation sections and the first and second inner divertors with quasi-dc low profile necking coils.

According to a further embodiment of the present disclosure, the method further comprising generating one of a magnetic dipole field and a magnetic quadrupole field within the chamber with saddle coils coupled to the chamber.

According to a further embodiment of the present disclosure, the method further comprising conditioning the internal surfaces of the chamber and the internal surfaces of first and second formation sections, first and second divertors interposing the confinement chamber and the first and second formation sections, and first and second outer divertors coupled to the first and second formation sections with a gettering system.

According to a further embodiment of the present disclosure, the gettering system includes one of a Titanium deposition system and a Lithium deposition system.

According to a further embodiment of the present disclosure, the method further comprising axially injecting plasma into the FRC from axially mounted plasma guns.

According to a further embodiment of the present disclosure, the method further comprising controlling the radial electric field profile in an edge layer of the FRC.

According to a further embodiment of the present disclosure, controlling the radial electric field profile in an edge layer of the FRC includes applying a distribution of electric potential to a group of open flux surfaces of the FRC with biasing electrodes.

According to a further embodiment of the present disclosure, the method further comprising injecting compact toroid (CT) plasmas from first and second CT injectors into the FRC plasma at an angle towards the mid-plane of the confinement chamber, wherein the first and second CT injectors are diametrically opposed on opposing sides of the mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, a system for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising a confinement chamber, first and second diametrically opposed FRC formation sections coupled to the confinement chamber, first and second diametrically opposed divertors coupled to the FRC formation sections, one or more of a plurality of plasma guns, one or more biasing electrodes and first and second mirror plugs, wherein the plurality of plasma guns includes first and second axial plasma guns operably coupled to the first and second divertors, the first and second formation sections and the confinement chamber, wherein the one or more biasing electrodes being positioned within one or more of the confinement chamber, the first and second formation sections, and the first and second outer divertors, and wherein the first and second mirror plugs being position between the first and second formation sections and the first and second divertors, a gettering system coupled to the confinement chamber and the first and second divertors, a plurality of neutral atom beam injectors coupled to the confinement chamber and angled toward a mid-plane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc coils positioned around the confinement chamber, the first and second formation sections, and the first and second divertors, and first and second set of quasi-dc mirror coils positioned between the first and second formation sections and the first and second divertors, and an antenna system positioned around the confinement chamber, wherein the antenna system is configured to launch high harmonic fast waves into the FRC plasma to heat plasma electrons.

According to a further embodiment of the present disclosure, the system is configured to generate an FRC and maintain the FRC without decay while the neutral beams are injected into the plasma and elevate the plasma electron temperature to about above 1.0 keV.

According to a further embodiment of the present disclosure, the antenna system includes one or more antennas positioned to launch the high harmonic fast waves at a launch angle from the mid-plane of the confinement chamber into the FRC plasma.

According to a further embodiment of the present disclosure, the launch angle is in a range of about 15° to about 25° from the mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, the launch angle is near but less than normal to a longitudinal axis of the confinement chamber.

According to a further embodiment of the present disclosure, the antenna system includes phased array antennas with a plurality of straps.

According to a further embodiment of the present disclosure, the high harmonic fast waves are fast waves in radio frequency ranges.

According to a further embodiment of the present disclosure, the system is configured to heat FRC plasma electrons from about 150 eV to above about 1 keV.

According to a further embodiment of the present disclosure, the first and second divertors comprise first and second inner divertors interposing the first and second formation sections and the confinement chamber, and further comprising first and second outer divertors coupled to the first and second formation sections, wherein the first and second formation sections interposing the first and second inner divertors and the first and second outer divertors.

According to a further embodiment of the present disclosure, the system further comprising first and second axial plasma guns operably coupled to the first and second inner and outer divertors, the first and second formation sections and the confinement chamber.

According to a further embodiment of the present disclosure, the system further comprising two or more saddle coils coupled to the confinement chamber.

According to a further embodiment of the present disclosure, the formation section comprises modularized formation systems for generating an FRC and translating it toward a mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, the biasing electrodes includes one or more of one or more point electrodes positioned within the containment chamber to contact open field lines, a set of annular electrodes between the confinement chamber and the first and second formation sections to charge far-edge flux layers in an azimuthally symmetric fashion, a plurality of concentric stacked electrodes positioned in the first and second divertors to charge multiple concentric flux layers, and anodes of the plasma guns to intercept open flux.

According to a further embodiment of the present disclosure, the system further comprising first and second compact toroid (CT) injectors coupled to the confinement chamber at an angle towards the mid-plane of the confinement chamber, wherein the first and second CT injectors are diametrically opposed on opposing sides of the mid-plane of the confinement chamber.

The example embodiments provided herein, however, are merely intended as illustrative examples and not to be limiting in any way.

All features, elements, components, functions, and steps described with respect to any embodiment provided herein are intended to be freely combinable and substitutable with those from any other embodiment. If a certain feature, element, component, function, or step is described with respect to only one embodiment, then it should be understood that that feature, element, component, function, or step can be used with every other embodiment described herein unless explicitly stated otherwise. This paragraph therefore serves as antecedent basis and written support for the introduction of claims, at any time, that combine features, elements, components, functions, and steps from different embodiments, or that substitute features, elements, components, functions, and steps from one embodiment with those of another, even if the following description does not explicitly state, in a particular instance, that such combinations or substitutions are possible. Express recitation of every possible combination and substitution is overly burdensome, especially given that the permissibility of each and every such combination and substitution will be readily recognized by those of ordinary skill in the art upon reading this description.

In many instances, entities are described herein as being coupled to other entities. It should be understood that the terms “coupled” and “connected” (or any of their forms) are used interchangeably herein and, in both cases, are generic to the direct coupling of two entities (without any non-negligible (e.g., parasitic) intervening entities) and the indirect coupling of two entities (with one or more non-negligible intervening entities). Where entities are shown as being directly coupled together, or described as coupled together without description of any intervening entity, it should be understood that those entities can be indirectly coupled together as well unless the context clearly dictates otherwise.

While the embodiments are susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that these embodiments are not to be limited to the particular form disclosed, but to the contrary, these embodiments are to cover all modifications, equivalents, and alternatives falling within the spirit of the disclosure. Furthermore, any features, functions, steps, or elements of the embodiments may be recited in or added to the claims, as well as negative limitations that define the inventive scope of the claims by features, functions, steps, or elements that are not within that scope. 

What is claimed is:
 1. A method for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising the steps of: forming an FRC about a plasma in a confinement chamber, injecting a plurality of neutral beams into the FRC plasma at an angle toward the mid-plane of the confinement chamber, and heating electrons of the FRC plasma with high harmonic fast waves propagating into the FRC plasma by launching a plurality of high harmonic fast waves from one or more antennas into the FRC plasma in the confinement chamber at a launch angle in a range of about 15° to about 25° from the mid-plane of the confinement chamber, wherein the high harmonic fast waves are fast waves in radio frequency ranges.
 2. The method of claim 1, wherein the one or more antennas is a phased array antenna with a plurality of straps.
 3. The method of claim 1, wherein the step of heating the electrons including heating the electrons from about 150 eV to above 1 keV.
 4. The method of claim 1, further includes maintaining the FRC at or about a constant value without decay while injecting beams of fast neutral atoms into the FRC plasma in the confinement chamber and elevating the plasma electron temperatures to above 1.0 keV.
 5. The method of claim 1, further comprising the step of generating a magnetic field within the confinement chamber with quasi dc coils extending about the confinement chamber and a mirror magnetic field within opposing ends of the confinement chamber with quasi dc mirror coils extending about the opposing ends of the confinement chamber.
 6. The method of claim 1, wherein the step of the forming the FRC includes forming a formation FRC in opposing first and second formation sections coupled to the confinement chamber and accelerating the formation FRC from the first and second formation sections towards the mid through plane of the confinement chamber where the two formation FRCs merge to form the FRC.
 7. A system for generating and maintaining a magnetic field with a field reversed configuration (FRC) comprising a confinement chamber, first and second diametrically opposed FRC formation sections coupled to the confinement chamber, first and second divertors coupled to the first and second formation sections, one or more of a plurality of plasma guns, one or more biasing electrodes and first and second mirror plugs, wherein the plurality of plasma guns includes first and second axial plasma guns operably coupled to the first and second divertors, the first and second formation sections and the confinement chamber, wherein the one or more biasing electrodes being positioned within one or more of the confinement chamber, the first and second formation sections, and the first and second outer divertors, and wherein the first and second mirror plugs being position between the first and second formation sections and the first and second divertors, a gettering system coupled to the confinement chamber and the first and second divertors, a plurality of neutral atom beam injectors coupled to the confinement chamber and angled toward a mid-plane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc coils positioned around the confinement chamber, the first and second formation sections, and the first and second divertors, and first and second set of quasi-dc mirror coils positioned between the first and second formation sections and the first and second divertors, and an antenna system including one or more antennas positioned around the confinement chamber adjacent the mid-plane of the confinement chamber, wherein the antenna system is configured to launch high harmonic fast waves into the FRC plasma at a launch angle in a range of about 15° to about 25° from the mid-plane of the confinement chamber, wherein the high harmonic fast waves are fast waves in radio frequency ranges.
 8. The system of claim 7, wherein the antenna system includes phased array antennas with a plurality of straps.
 9. The system of claim 7, wherein the high harmonic fast waves are fast waves in radio frequency ranges.
 10. The system of claim 7, wherein the system is configured to heat FRC plasma electrons from about 150 eV to above 1 keV.
 11. The system of claim 7, wherein the system is configured to generate an FRC and maintain the FRC without decay while the neutral beams are injected into the plasma.
 12. The system of claim 11, wherein the system is configured to elevate FRC plasma electron temperature above 1 keV.
 13. The system of claim 7, wherein the first and second divertors comprise first and second inner divertors interposing the first and second formation sections and the confinement chamber, and further comprising first and second outer divertors coupled to the first and second formation sections, wherein the first and second formation sections interposing the first and second inner divertors and the first and second outer divertors, and further comprising one or more of first and second axial plasma guns operably coupled to the first and second inner and outer divertors, the first and second formation sections and the confinement chamber, and two or more saddle coils coupled to the confinement chamber. 